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A meromorphic projective structure on a punctured Riemann surface $X\setminusP$ is determined, after fixing a standard projective structure on $X$, by ameromorphic quadratic differential with poles of order three or more at eachpuncture in $P$. In this article we prove the analogue of Thurston's graftingtheorem for such meromorphic projective structures, that involves graftingcrowned hyperbolic surfaces. This also provides a grafting description forprojective structures on $\mathbb{C}$ that have polynomial Schwarzianderivatives. As an application of our main result, we prove the analogue of aresult of Hejhal, namely, we show that the monodromy map to the decoratedcharacter variety (in the sense of Fock-Goncharov) is a local homeomorphism.

Meromorphic projective structures, grafting and the monodromy map